While I know of no way to move both the audio and video tracks up or down together, I can offer two ways get them on the desired tracks in the first place:
- when dragging, hover the mouse over the track you want to the clip to land on
- In the Timeline, set Source Patching to the desired tracks, then use the Insert or Overlay command instead of drag-n-drop.
Once a clip is in a sequence on the "wrong" track, as far as I'm aware you're stuck moving the audio and video separately. I encourage you to submit a feature request: www.adobe.com/go/wish (and that's not just a canned suggestion; I'd love to have a shortcut for doing this!)